Change

In philosophy, change refers to a difference in a state of affairs at different points in time. The Presocratic philosopher Heraclitus was the first to deal with the matter of change, stating that "One cannot step into the same river twice," as the river will have changed after the person has stepped into it the first time.

History
The Greek Presocratic philosopher Heraclitus was the first known philosopher to discuss change, stating that "a man cannot step in the same river twice." After a person steps in a river, the waters are very slightly changed, and its state before the person stepped into it has changed since the person stepped in the river.

Parmenides and the Eleatics raised a number of profound problems which caused them to conclude that change was impossible, that change was one and unchanging. Parmenides considered the very notion of non-existence to be absurd, believing that "from nothing comes nothing". The more radical point was that something was not material, but just a general predicate; Parmenides rejected changes in coloring, as the new color comes into existence from nothing. Parmenides' follower Zeno of Elea argued that, in order to move from A to B, one must make it halfway from A to B, and halfway to that half, and so on, believing that motion would consist of an infinite number of steps; this, he held, was impossible.

The Eleatic view has since been defeated by future philosophers, with the atomism of Democritus responding to the Eleatic notion that change is impossible. Democritus hypothesized that every visible object was composite of several unseen, eternal objects (atoms). Anaxagoras argued that a number of eternal primal ingredients mixed together in a continuum would make up objects; Aristotle accepted this view. No material object was made of a pure ingredient, instead consisting of various.

Ship of Theseus
The problem of change and identity is present in the "Ship of Theseus". In ancient times, there was a ship named for King Theseus of Athens, and the ship became weak over the years. Its old boards were replaced with new ones and its mast was replaced with a new one, and it had all new boards and masts within 50 years. Philosophers questioned whether the same ship that was in the harbor 50 years ago was the same ship, as it had completely changed. This applies to humans, as people change a lot between their teenage years and when they grow up. There has to be one person who underwent the change, meaning that the person has always existed, instead with changing properties; this is Anaxagoras' continuum, confirmed by Aristotle. The idea of continuity - of time being a continuum and of an object being continuous - is an answer to the issue, as is the argument that the completely-changed ship is no longer the Theseus. If everyone purchased the old ship's materials (kept in a warehouse) and built a ship according to the same plans as the original Theseus, some could argue that this third ship is the real Theseus. There is the question of whether or not the third, reconstructed ship is the same as the original (pre-renovation) Theseus is the same, or whether the original Theseus is the same as the renovated ship. The main question is: how could anybody say that the renovated Theseus or the reconstructed Theseus is the same as ship one, when that would mean that the two newer ships are the same? Whenever one makes an identity claim, claiming that two things are the same, one almost always makes two different descriptions. The two new ships are one and the same thing under two different descriptions.

Gottfried Leibniz came up with a solution to the problem, known as "Leibniz's Law". It argues that some ships are the same if they have the same properties or relations. Whether the ship is the same or not depends on the purpose of the word "same"; if the original ship was stolen property, and the owner demanded that it be returned, which ship would be returned to him? The original owner would be entitled to the third ship, as he did not purchase the materials for Ship 2. However, if the crew of the renovated ship remained the same as the original ship, the admiral would recognize the renovated ship as the Theseus. In addition, the history of the ship could continue with any of the ships, as objects can be considered the "same" for one purpose, yet different for another.